The invention is based on a fuel injection pump for internal combustion engines. In a known fuel injection pump of this type, two pump plungers located side by side are provided in one pump housing, each plunger being driven by a separate camshaft. Each plunger pumps into a single fuel injection line assigned to it and leading to a fuel injection valve on an associated internal combustion engine. The injection quantity is controlled via a common overflow conduit, which can be opened by means of a magnetic valve to provide a relief volume. The pump plungers also execute their pumping strokes in alternation, and a slide valve control is provided so that the fuel quantity pumped at high pressure by one plunger cannot flow out to the relief side during the intake or filling stroke of the other plunger. The pump plunger itself, with a control edge, acts as the valve slide. Alternatively, check valves are also provided, some of them in the fuel fill line of the various pump work chambers. Thus, the known fuel injection pump is designed in the manner of an inline injection pump, in which each pump plunger serves to supply fuel to one injection site.